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Factoring an integer with three oscillators and a qubit.

Lukas Brenner1,2, Libor Caha3,4, Xavier Coiteux-Roy5,6,7,8,9

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This study introduces a novel quantum factoring algorithm using hybrid qubit-oscillator systems. This approach offers a device-independent method for quantum computation, achieving polynomial time complexity.

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Area of Science:

  • Quantum Computing
  • Quantum Information Science
  • Algorithm Design

Background:

  • Traditional quantum algorithm design often relies on the abstraction of a universal quantum computer with scalable qubits.
  • This model, while useful for device-independent development, may not fully leverage the benefits of specific physical setups.
  • Hybrid qubit-oscillator systems offer an alternative framework for quantum computation.

Purpose of the Study:

  • To explore the benefits of a physical setup-centered approach in quantum algorithm design.
  • To develop a quantum factoring algorithm utilizing hybrid qubit-oscillator systems.
  • To demonstrate native realizations of essential quantum operations within such systems.

Main Methods:

  • Utilizing hybrid qubit-oscillator systems with linear optics and qubit-controlled Gaussian unitaries.
  • Implementing native continuous variable Fourier transforms and arithmetic operations.
  • Developing a quantum factoring algorithm based on these physical realizations.

Main Results:

  • A polynomial-time quantum factoring algorithm was developed.
  • The algorithm requires minimal resources: only one qubit and three oscillators.
  • The algorithm's efficiency is independent of the magnitude of the number being factored.

Conclusions:

  • A physical setup-centered approach can yield significant benefits in quantum algorithm design.
  • Hybrid qubit-oscillator systems provide a powerful platform for efficient quantum computation.
  • This work demonstrates a practical and resource-efficient quantum factoring algorithm.